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Fraction Calculator

Add, subtract, multiply, or divide two fractions and see the reduced answer, decimal form, and working steps.

Simplified fraction

5/6

Decimal value: 0.8333

Inputs use whole numbers. Non-integer values are truncated before calculation.

Quick Answer

To add or subtract two fractions, give them a shared denominator, then combine the numerators; to multiply, multiply tops and bottoms; to divide, flip the second fraction and multiply. For example, 1/2 + 1/3 becomes 3/6 + 2/6, which is 5/6. This calculator does each step and reduces the answer to lowest terms, with a decimal form too.

How A Fraction Calculator Works, Step By Step

A fraction calculator solves math with two fractions and gives the answer in lowest terms. The tool uses the top number, bottom number, and math sign to add, subtract, multiply, or divide. For add and subtract work, the tool makes a shared bottom number, then joins the top numbers. For multiply work, it multiplies the top numbers and then the bottom numbers. For divide work, the tool flips the second fraction and multiplies. After the math step, the tool reduces the result by the largest whole number both parts share. The tool also shows a decimal form, so you can read the same result another way. This helps with homework, recipes, tape measures, craft plans, and any case where you need to check or compare a fraction answer.

Fraction Calculator: The Formula Behind The Result

For two fractions a/b and c/d, the calculator uses these formulas.

  • Add: a/b + c/d = (a x d + c x b) / (b x d).
  • Subtract: a/b - c/d = (a x d - c x b) / (b x d).
  • Multiply: a/b x c/d = (a x c) / (b x d).
  • Divide: a/b / c/d = (a x d) / (b x c).
  • Simplify: divide the result numerator and denominator by their greatest common divisor.

In these formulas, a and c are the top numbers. The letters b and d are the bottom numbers. A bottom number cannot be zero because division by zero has no defined value.

Using The Fraction Calculator: Step By Step

Inputs

  • Numerator 1: the top number in the first fraction.
  • Denominator 1: the bottom number in the first fraction.
  • Operation: add, subtract, multiply, or divide.
  • Numerator 2: the top number in the second fraction.
  • Denominator 2: the bottom number in the second fraction.

Steps

  1. Enter the numerator and denominator for the first fraction.
  2. Choose the operation you want to run.
  3. Enter the numerator and denominator for the second fraction.
  4. Read the simplified fraction in the result box.
  5. Check the decimal value if you need a decimal form.

Fraction Calculator In Practice: A Real Example

What is 1/2 + 1/3?

  1. Formula with values: 1/2 + 1/3 = (1 x 3 + 1 x 2) / (2 x 3).
  2. Multiply across for the shared denominator form: 2 x 3 = 6.
  3. Multiply the first numerator by the second denominator: 1 x 3 = 3.
  4. Multiply the second numerator by the first denominator: 1 x 2 = 2.
  5. Add the adjusted numerators: 3 + 2 = 5.
  6. Write the fraction: 5 / 6 = 5/6.
  7. Check lowest terms: the greatest common divisor of 5 and 6 is 1, so 5/6 is already simplified.
  8. Decimal value: 5 / 6 = 0.8333333333.
  9. Rounding: the decimal result is shown to four decimal places, so 0.8333333333 rounds to 0.8333.

1/2 + 1/3 = 5/6, or 0.8333 as a decimal.

When To Use A Fraction Calculator (Or Not)

Use this tool when both inputs are fractions with whole-number top and bottom values. It works for proper fractions, fractions greater than one, and negative fractions.

Use it to check fraction math, reduce an answer to lowest terms, or compare a fraction answer with its decimal form. For mixed numbers, change the mixed number to a fraction greater than one before using the tool.

A fraction can stand for a part of a cup, a mark on a tape, or a share of a score. The math stays the same when the unit changes. Use the result as a check before you copy it into class work or a plan. The fraction line shows the exact share. The decimal line helps when you need to compare sizes fast.

If a value looks odd, check each input box. A zero in a bottom box will stop the math. A minus sign can go on the top or the bottom. The tool moves the sign to the top. That keeps the final form neat.

For related checks, the math calculators hub groups the basic tools, the formula reference lists the equations, and the glossary defines common math terms.

Assumptions

  • Inputs are treated as whole numbers.
  • A denominator cannot be zero.
  • The calculator returns an improper fraction when the result is greater than one.
  • Negative signs are normalized to the numerator.
  • Decimal output is rounded for display.

The exact fraction is the primary answer. The decimal is a rounded display form when the value repeats, so use the simplified fraction when exactness matters.

Limitations

  • The calculator does not accept mixed-number notation directly.
  • Non-integer inputs are truncated before calculating.
  • The decimal value may be rounded when the fraction has a repeating decimal.
  • The tool handles two fractions at a time.

In Practice

The most common mistake is adding the bottoms as well as the tops, so 1/2 + 1/3 becomes 2/5. That is wrong: only the numerators combine once the denominators match. Always find a shared denominator first, and remember multiplication and division do not need one, which is why they often feel easier than addition.

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Frequently Asked Questions About Fraction Calculator

How does a fraction calculator add fractions?

A fraction calculator adds fractions by making a shared bottom number and joining the changed top numbers. For 1/2 + 1/3, it uses 6 as the bottom number, then adds 3/6 and 2/6 to get 5/6.

Why does the calculator simplify the fraction?

The tool reduces the fraction so the result is in lowest terms. It divides the top and bottom numbers by their largest shared factor, which keeps the value the same and makes the fraction easier to read.

What is the rule for dividing fractions?

Dividing fractions means multiplying the first fraction by the flipped second fraction. For a/b divided by c/d, the tool uses a/b x d/c, which gives (a x d) / (b x c).

Can the calculator handle improper fractions?

The fraction calculator can handle answers greater than one, such as 7/4 or 9/5. If the final result is greater than one, the tool keeps the answer as a fraction and also shows the decimal form.

Is a simplified fraction the same value?

A simplified fraction has the same value as the original fraction. Dividing the top and bottom numbers by the same nonzero number changes the form, not the amount the fraction represents.

Why show both a fraction and a decimal answer?

The fraction answer shows the exact result, while the decimal answer helps with quick comparison. For 5/6, the fraction stays exact, and the decimal rounds to 0.8333. Both forms point to the same value.

Sources

Last updated: . Reviewed for accuracy against the formula shown above.